Human identification using pyroelectric infrared sensors
Transcript of Human identification using pyroelectric infrared sensors
UNLV Theses, Dissertations, Professional Papers, and Capstones
5-2009
Human identification using pyroelectric infrared sensors Human identification using pyroelectric infrared sensors
Aron E. Suppes University of Nevada, Las Vegas
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HUMAN IDENTIFICATION USING PYROELECTRIC
INFRARED SENSORS
by
Aron Edward Suppes
Bachelor of Science Computer Science Hawaii Pacific University
2005
A thesis submitted in partial fulfillment of the requirements for the
Master of Science Degree in Computer Science School of Computer Science
Howard R. Hughes College of Engineering
Graduate College University of Nevada, Las Vegas
May 2009
UMI Number: 1484373
All rights reserved
INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted.
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Copyright by Aron Edward Suppes 2009 All Rights Reserved
•IIM»JJ.MLl'I.IJJUt)MII.UMjll.l-l
Thesis Approval The Graduate College University of Nevada, Las Vegas
APRIL 3rd _,2009_
The Thesis prepared by
ARON EDWARD SUPPES
Entitled
HUMAN IDENTIFICATION USING PYROELECTRIC SENSORS
is approved in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE IN COMPUTER SCIENCE
Examination Committee Member
Examination Committee Member
Gjaduat^College Faculty Representative
Examination Committee Chair
Dean of the Graduate College
1017-53 11
ABSTRACT
Human Identification Using Pyroelectric Infrared Sensors
by
Aron E. Suppes
Dr. Evangelos Yfantis, Examination Committee Chair Professor of Computer Science
University of Nevada, Las Vegas
The objective of this thesis is to discuss the viability of using pyroelectric
infrared (PIR) sensors as a biometric system for human identification.
The human body emits infrared radiation, the distribution of which varies
throughout the body, and depends upon the shape and composition of the
particular body part. A PIR sensor utilizing a Fresnel lens will respond to this
infrared radiation. When a human walks, the motion of the body's individual
components form a characteristic gait that is likely to affect a PIR sensor field in a
unique way.
A statistical model, such as a Hidden Markov Model, could be used for the
identification process. The model would consist of two phases; learning and
testing. The learning phase would train the model on a particular feature or
signature. The testing phase would take a signature as input and determine
which of the trained models it matches with the highest probability.
iii
TABLE OF CONTENTS
APPROVAL PAGE ii
ABSTRACT iii
LIST OF FIGURES vi
LIST OF TABLES vii
ACKNOWLEDGMENTS viii
CHAPTER 1 INTRODUCTION 1
CHAPTER 2 BACKGROUND .3
Gait for Human Identification 3 Infrared Radiation and the Human Body 4 Measuring Gait using Infrared Radiation 4
CHAPTER 3 METHODOLOGY 6 Sensor Module 6
Pyroelectric Infrared (PIR) Sensor 6 Fresnel Lens Array 8
Motion Detection Circuit 8 Dwell Time 9 Retriggering 9 Circuit Design 10 Signal Generation 12 Decay 13
Digital Signal Processing 14 Analog to Digital Conversion 14
Feature Generation 15 Normal Distribution 16 Thresholding 17
iv
Low-pass Filtering 19 Temporal Pattern Recognition 20
Classification 20 Hidden Markov Models (HMM) 21
HMM Parameters 22 Forward Algorithm 24 Backward Algorithm 25 Forward-Backward Algorithm.. 26
Model Training 29 Model Testing 29
Maximum Likelihood 30
CHAPTER 4 DATA ANALYSIS 31 Configuration 31
Microcontroller 32 PIR Identification Application 34
Initial Testing 35 Experiment 41
CHAPTER 5 CONCLUSIONS 44
BIBLIOGRAPHY 47
VITA 48
v
LIST OF FIGURES
Figure 1. Schematic for motion detection circuit 11 Figure 2. The component side of the motion detection circuit 12 Figure 3. The sensor side of the motion detection circuit 12 Figure 4. Signal as it decays with respect to time 14 Figure 5. Waveform showing decay 18 Figure 6. Sensor module 31 Figure 7. PIR stand with four sensor modules 32 Figure 8. Schematic of Analog-to-Digital converter 33 Figure 9. Demo board containing Javelin Stamp and ADC 34 Figure 10. PIR Human Identification Application 35 Figure 11. Experiment walking path 36 Figure 12. Signal generated from sensor 1 37 Figure 13. Signal generated from sensor 2 37 Figure 14. Signal generated from sensor 3 38 Figure 15. Signal generated from sensor 4 38 Figure 16. Sample means for three subjects 40 Figure 17. Sample standard deviations for three subjects 40
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ACKNOWLEDGEMENTS
Special thanks to all the people who helped me complete this thesis. In
particular I would like to thank Ghada, Josh, and Shirin for their patience and
understanding. I would also like to thank my examination committee, in particular
Dr. Evangelos Yfantis for all his help.
viii
CHAPTER 1
INTRODUCTION
A biometric system relies on pattern recognition for the measurement and
analysis of unique physical or behavioral characteristics as a means of verifying
personal identity. Many aspects of human form and behavior are characteristic
and therefore, suitable for identification purposes. Typical biometrics may
include the fingerprint, face, hand, iris, DNA, signature, gait, and voice. Biometric
systems work by measuring a particular biometric using a sensor and then
transforming the sensed data into a digital feature.
Human gait has been shown to be a characteristic trait of human behavior
that can be used for identification. For analysis, a person's gait must first be
recorded, typically using a video camera. Image processing techniques are then
utilized to measure the principal components of the human gait as they change
over time. The relative expense of video cameras and the supporting data
systems make their use somewhat limited and impractical for many common
tasks.
Pyroelectric (PIR) sensors have been used for many years as a primary
component of motion detection devices. These sensors and the associated
electronics are widely available and very inexpensive. These sensors work by
detecting the infrared radiation released from the human body. When a human
1
walks, the motion of the body's individual components are likely to affect a PIR
sensor field in a unique way. Measuring gait with sensors such as these is
desirable because of the low system costs and data loads. The objective of this
paper is to discuss the viability of measuring the human gait as a biometric for
human identification, using pyroelectric infrared (PIR) sensors.
2
CHAPTER 2
BACKGROUND
Gait for Human Identification
Gait refers to the manner of walking or running. It has been shown that
humans have the capability of recognizing people from a distance solely based
on their gait. This work seems to suggest that there must be some sort of
characteristic nature to a person's gait, which if properly extracted, could be used
by a biometric system for identification purposes.
For normal walk, gait sequences are repetitive and exhibit nearly periodic
behavior, particularly in the movement of the legs and in the swing of the arms.
While a person's gait may seem random and unpredictable, studies have shown
that there are 24 different components to human gait and that if all movements
are considered, gait is unique. There are two aspects to human gait that need to
be measured in order for it to be distinctive; structural content and dynamic
content. Structural content includes data obtained from the shape of the
subject's profile taken at successive frames to show how it changes over time.
Dynamic content includes data obtained from measurements that focus on the
velocity of the subject's motion. While distinct, both types of information are
required for the gait to be characteristic and therefore, cannot be decoupled.
3
Infrared Radiation and the Human Body
All objects radiate energy continuously in the form of electromagnetic waves
due to the thermal vibrations of their molecules. As such, any object that has a
temperature above absolute zero is known to emit electromagnetic radiation at
some wavelength, with the wavelength being directly proportional to the
temperature of the object. We can calculate the peak wavelength of the radiation
emitted by an object, such as the human body, by taking advantage of this
known relationship between wavelength and temperature called Wein's
displacement law:
(0.2898 x 10_2m x °K ) h-max = \ ^ 1 T = temperature of object in °K>
The temperature of the skin of a typical human being is approximately 34 °C. By
converting this temperature to Kelvin, we can determine the peak wavelength as:
_ 0.2898 xlO _ 2mx°K Xmax " 307^K
^max « 9.5 x 10"6m or 9.5 \im
Thus, it can be shown that the black body radiation emitted by a person peaks
between 9 to 10 |am, which lies in the infrared (IR) portion of the electromagnetic
spectrum.
Measuring Gait using Infrared Radiation
In order for a person's gait to be analyzed, it must first be recorded or sensed
in some way. Typically, video cameras are set up to record the movements while
image processing techniques are utilized to measure the principal components of
4
the human gait. Another method, which is the topic of this paper, is to utilize a
person's emitted infrared radiation as a way to measure their gait.
There are many factors to consider when designing a biometric system, the
primary one in many cases being cost. Visible light and infrared cameras are
relatively expensive and also have drawbacks including high data loads to
transfer and store video and large computational costs to perform the necessary
image processing. Pyroelectric sensors, on the other hand, potentially offer a
much cheaper method of human detection and/or identification. They also would
involve much lighter data loads, computational costs, and cheaper system costs.
As we have already discussed, the human body radiates energy in the near-
infrared, approximately 9 to 10 (irn. This radiation, however, is not constant as
the human body is irregularly shaped and due to movement, its overall surface
area will change relative to a common point. From the point-of-view of a PIR
sensor, the magnitude and duration of the IR energy detected can be used to
track this movement in the spatial domain.
Due to its complex geometry and the way heat is radiated to the environment,
the human body can be viewed as a distributed IR source that varies both in time
and in the spatial domain. Therefore, it seems plausible to assume that
recognizing how a person's infrared signature varies over space and time as they
walk, may correlate with their gait.
5
CHAPTER 3
METHODOLOGY
Sensor Module
Many PIR sensor modules are commercially available, but these are typically
built for use as devices that simply detect motion and close a relay for an
external lighting or alarm circuit. These devices are unsuitable for human
identification purposes. What is needed for our experiment is a package that
contains a dual-element sensor, motion detection circuit, and a Fresnel lens
array. We will refer to this package as a sensor module.
For this experiment, we chose commercially available motion detectors that
contained a PIR sensor and circuit board located in a molded plastic package
with an attached Fresnel lens array. The PIR sensor and circuit board were
discarded and replaced with a purpose-built motion detection circuit that is more
suited for human identification applications. The following sections will describe
each of these components more thoroughly.
Pvroelectric Infrared (PIR) Sensor
A pyroelectric infrared (PIR) sensor is a device that generates a surface
electric charge in response to being exposed to infrared radiation. The sensor
used in this experiment is the PIR325, available from the Glolab Corporation.
6
The sensor package consists of a sensing element, a field-effect transistor (FET),
and an infrared filter.
The sensing element of a PIR sensor is composed of a crystalline material
that possesses the pyroelectric property. Pyroelectricity is defined as the ability
to generate an electric potential when exposed to changes in temperature. The
amount of electric potential generated by the charge from the sensing element is
usually very small, on the order of 1 mV. This flow of electric charge drives a
field-effect transistor (FET).
The crystalline material used in the sensing element is sensitive to a wide
range of radiation. PIR sensors used for motion detection generally are only
interested in the band with which the human body radiates; approximately 8 to 14
urn, with a peak wavelength of approximately 9.5 ^m. The sensor package
includes an infrared filter to limit the incoming radiation to this range for this very
purpose.
For the purposes of detecting motion, the sensor package includes two
sensing elements, referred to as a dual-element sensor. This is necessary to
offset signals caused by direct sunlight, changing room temperature, and
vibration from generating a voltage. This is accomplished by connecting the two
sensing elements in series opposition. With this configuration, the voltage
produced by the sensor is the difference of the voltage produced by both of the
sensing elements. The sensing elements are oriented along the horizontal plane
within the sensor package. The energy being radiated from an object passing in
front of the sensor will invariably reach one of the sensing elements before the
7
other, thereby causing a positive or negative voltage to be induced. Any
radiation that strikes both sensing elements at the same exact time will generate
the same voltage in both sensing elements and therefore will be cancelled.
Fresnel Lens Array
Fresnel lenses are typically used in motion detectors to focus infrared
radiation onto the sensing elements of a PIR sensor. A Fresnel lens can capture
more infrared radiation and focus it onto a smaller point on the PIR sensing
element. This focal point moves across the sensor as the IR source moves and
exposes one element at a time. The use of a Fresnel lens can increase the
maximum distance of detection from a few meters to approximately 30 meters
and provide more stable detection.
Fresnel lenses share all the optical characteristics of a conventional plano
convex lens but are physically quite different. A Fresnel lens array is a single
molded piece of plastic that is transparent to infrared radiation but only
translucent to visible radiation. This piece of plastic has multiple individual
Fresnel lenses molded into it. They are used to produce a broad, tailored field of
view through many repeated narrow fields of view.
Motion Detection Circuit
In order to generate a characteristic digital signature using a motion detector,
the circuit that implements motion detection must exhibit certain characteristics.
Namely, a low dwell time and a fast trigger time. Each of these topics will be
covered in the following sections.
8
Dwell Time
Dwell is the amount of time that a circuit remains on after motion is detected.
For example, in a conventional motion detection circuit it may be desired to use a
relay to close an external circuit once motion is detected, such as an outdoor
lighting circuit. In this circumstance, you would want a dwell time equal to the
amount of time that the lighting circuit should be closed and the lights to remain
on. For the purposes of digital signature generation, the dwell time should be
less than the polling interval of the device that's checking the state of the motion
detector. If this is not the case, a single motion detection event will appear in the
digital feature as multiple samples. This would reduce the resolution of the
system and increase network traffic and storage requirements with redundant
information. The details of these processes will be discussed in the next section.
Retrigqerinq
A circuit's ability to retrigger is a timing issue that describes whether, and how
fast it, can generate a motion detection event after a preceding motion detection
event. Using the outdoor lighting circuit example from above, a fast trigger may
be unnecessary if the idea is to close an external circuit for a relatively long time
once a motion detection event has occurred. In this circumstance, a motion
detection event will initially close the circuit for a length of time determined by the
dwell time of the circuit. Retriggering the circuit while it is in dwell is unnecessary
because the external lighting circuit is already closed and on. In this case, the
circuit can effectively ignore multiple repeated motion detection events. Stated
9
more clearly, the time to retrigger the circuit should be greater than or equal to
the circuit's dwell time. For the purposes of digital signature generation, a fast
retriggering of the circuit is necessary, in part because of the circuit's requirement
of a fast dwell time. It is also desired to encapsulate a single motion detection
event in a single sample when polling. A fast trigger prevents the device that is
polling the motion the state of the motion detector from sampling a single motion
detection event multiple times, thereby increasing resolution and decreasing
network bandwidth and storage requirements. The need for fastest trigger
possible eliminates the need for a timing circuitry to be added to the motion
detection circuit, usually implemented as an integrated circuit. In this case, the
circuit's time to retrigger is determined by the amount of time needed by the
sensing elements to build up the necessary charge to drive the on-board field-
effect transistor in the motion sensor package. This is the fastest possible
retrigger time for the circuit and is determined by the individual sensor's physical
limitations of its sensing elements and the resistive and capacitive elements of
the circuit. This fundamentally provides an upper-bound on how fast the circuit
can effectively be polled.
Circuit Design
Commercially available motion detection circuits are designed for a much
different purpose than human identification and as such, are not robust enough
to perform this task. For this experiment, four motion detection circuits were built
for this specific purpose. The motion detection circuit is powered by a +5V power
supply, connected to the drain pin of the PIR325 sensor (see Figure 1). As
10
stated above, the voltage generated by the PIR325 sensor in response to a
motion detection event is low, approximately 1 mV, thus amplification is
necessary. This is accomplished using a LM324 operational amplifier in two
stages. A capacitor is placed across the power supply and ground to prevent
oscillation. In addition, a 100K pull-down resistor connected across the PIR325s
source pin to ground. This keeps the output of the circuit at approximately 0 V
when no motion is detected. Below is a schematic of the motion detection circuit:
PIR
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T 1 Drain
2 Source
3 Ground
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Figure 1. Schematic for motion detection circuit.
Two photographs, one of the sensor side and another of the component side of
the motion detection circuit are shown in the figures below:
11
Figure 2. The component side of the motion detection circuit.
Figure 3. The sensor side of the motion detection circuit.
Signal Generation
The output of the motion detection circuit is an analog signal whose strength
is relative to the amount of charge generated by the elements of the motion
sensor, which in turn represents the amount of infrared radiation striking them.
12
When power is initially applied to the circuit, the capacitive elements must reach
a stable state, which will cause the circuit's output to be unstable. After
approximately 30 seconds the circuit will stabilize, generating approximately 0 V
when no motion is detected. During a motion detection event, the charge
generated by the PIR sensing elements will drive a FET which will produce
output. The resulting signal will be amplified 72 dB using a LM324 op-amp. This
will produce a peak voltage of 3.9V. Due to the motion of the object passing in
front of the sensor, a voltage will be induced in one sensing element before the
other, producing a positive or negative voltage. As the object moves, the voltage
will be induced in the other sensing element and the voltage will alternate.
Decay
The amplitude of the resulting positive and negative spikes will vary based on
the magnitude of the infrared radiation detected by the sensing elements, with
the peak being +-3.9 V. If motion is suddenly stopped, the signal will begin to
decay to 0 V. This decay is a function of the resistive and capacitive elements in
the circuit and therefore is impossible to completely eliminate. This unwanted
decay can have the detrimental effect of potentially causing the device polling the
motion detector to register a motion detection event on a decaying signal. An
example of this can be shown in the following example:
13
Figure 4. Signal as it decays with respect to time.
The effects of decay can be reduced to acceptable levels through the use of
signal processing, which will be discussed later in this chapter.
Digital Signal Processing
The output of the motion detection circuit will be an analog signal. In order to
input this signal to a computer for the purposes of extracting a characteristic
digital feature, it must be processed. The signal processing techniques used in
this experiment include analog-to-digital conversion, noise detection,
thresholding, and low-pass filtering. The following sections will describe each of
these techniques more thoroughly.
Analog to Digital Conversion
The signal that is generated by the motion detection circuit is analog and
represents how the voltage generated by a PIR sensor varies with time. For this
signal to be analyzed by a digital computer, it must first be converted to digital
form. This process is known as analog-to-digital conversion (ADC).
14
When converting an analog signal to a digital form, there are two important
processes to consider: sampling and quantization. Sampling refers to the
process of converting the independent variable (time in this case) from
continuous to discrete.
Quantization, on the other hand, converts the dependant variable (voltage in
this case) from continuous to discrete. With respect to the motion detection
circuit, the continuous range of voltage values contained in the analog signal
must be approximated by an 8-bit integer, with values ranging from 0 to 255.
This approximation results in an inevitable error that can be as high as ± 0.5 LSB
(Least Significant Bit). Quantization results in the addition of a specific amount of
random noise and is uniformly distributed and possesses a mean of zero. Since
the uncorrelated noise in a system is additive, the noise generated by
quantization will simply add to whatever noise is already present in the analog
signal.
Feature Generation
Once the motion vector has been digitized and corrected for noise, it will
consist of integers that can range from 0 to 255 that represent a voltage between
-5V and +5V, with 127 being the zero reference or 0V. It is important to note that
the polarity of the voltage at any point is irrelevant; it simply corresponds to a
particular sensing element in a dual element sensor receiving infrared radiation a
moment before the other sensing element. What is important is the magnitude or
intensity of the radiation. For example, there is no important difference between -
2V and +2V when it comes to generating a feature, as they both correspond to
15
the same intensity of infrared radiation emitted from the source. Therefore, at
this point it would be advantageous to adjust the signal so that the number 0 will
provide the reference point of OV, while using the absolute values to eliminate
any notion of polarity. Subtracting 127 from the digital number and then taking
the absolute value can accomplish this as shown in the following formula:
y = {abs(x - 127) | x = old DN.y = new DN}
The resulting motion vector will consist of integers in the range 0 -127 .
Normal Distribution
Unlike a square wave or a triangle wave, for example, the waveform created
by a motion event has a random appearance. This is due to minor differences in
intensity of the infrared source, as well as a random temporal element due to the
unpredictable and often unrepeatable exact speed of motion of the source with
respect to the position of the sensor. This randomness means that the signal will
have a bell-shaped probability density function (pdf) that approximates a
Gaussian curve, or said to be normally distributed.
The fact that the underlying process exhibits a normal distribution provides
two parameters that allow us to characterize the signal, the mean and the
standard deviation. The mean describes the peak of the Gaussian curve and is
of the form:
The mean represents the average value of the signal. It is also commonly
referred to as the signal's DC component.
16
The standard deviation of a signal describes the breadth of the Gaussian
curve and represents the average amount of variance between the individual
values and the mean, and is of the form:
a =
N
N t=i
Utilizing the mean and the standard deviation will allow us to perform the
thresholding step described in the next section.
Thresholding
Thresholding describes the process of converting a digital value with an
arbitrary range (i.e. 8 bit) into a binary value represented by either a 0 or 1.
Thresholding is critical step in the generation of a digital feature as it involves the
separation of the carrier signal from the information contained within it.
In order to fully understand why the signal behaves the way it does, it is
necessary to review how it is generated. When a PIR sensor detects a motion
event, a voltage is generated which is measured by the onboard circuit. The
instant this peak voltage is generated, it begins to decay. This decay will cause
the signal to ramp down until either another motion event is detected, or the
resistive and capacitive elements of the circuit reach equilibrium and zero voltage
is present in the circuit. This decaying signal represents a voltage present in the
circuit and therefore will generate a digital number in the analog to digital
conversion process. The following figure shows an example waveform that
17
represents a motion vector, in which it is easy to see this decaying process
between peaks:
Figure 5. Waveform showing decay.
This decay means that during a repetition of motion events, the signal will very
rarely show a value of OV. This means that when generating a binary-valued
signal using thresholding, it is not practical to simply assign a value of 1 when a
voltage is present and a 0 otherwise. This would result in a binary signal that
would contain all 1s for a motion event and Os when no motion is detected
(although due to the white noise generated by the electronics as discussed in a
previous section, there exists a high probability that a voltage, regardless of how
small, will be present in the circuit.) In order to separate the information from the
signal, a more sophisticated algorithm must be employed.
The key to thresholding lies in understanding the underlying process that
generates the signal. The parts of the signal with the utmost interest are the
peaks, as these are representative of a motion event. The decaying signal is
18
representative of a type of noise that is not characteristic of the underlying
process. This noise will blend in with the white noise already present in the
system. Ideally we would like to design a thresholding function that captures the
higher amplitude peaks and ignores the lower amplitude areas between the
peaks. This function should generate a binary-valued sequence of alternating 1s
and Os that should be representative of a human motion feature.
By sampling the white noise present on the system, we can design a
thresholding function that can exclude this noise and capture the information
contained in the signal. This thresholding function must be proportional to the
noise level of the system. By first calculating the mean, and then the standard
deviation of the white noise, it is possible to form a threshold wherein only values
that lie above a particular amplitude are allowed to generate a binary 1. This
method provides a way to reliably extract the information generated by the
underlying process from the noisy signal.
Low-pass Filtering
The output of the thresholding function creates a binary signal, but this signal
still contains many high-frequency components that were contained in the
original signal. These high-frequency components are indicative of noise present
in the system. What we are interested in is the overall motion event contained in
the signal. For this reason, we pass the signal through a low-pass filter.
The filter we used is simply an averaging filter that is designed to reduce the
high-frequency components of the signal by smoothing. It is implemented by
using a spatial mask that encompasses a value and its two neighbors to either
19
side. A new value corresponding to the original value is arrived at by adding the
original's binary value to the values of its four neighbors, and then dividing by
five.
Temporal Pattern Recognition
Once we have extracted the features or digital signatures from the dataset
derived from the motion sensor array, we must employ a classification
mechanism to aid in pattern recognition.
Hidden Markov Models were chosen as the statistical model in this
experiment, primarily because they are well suited for applications in temporal
pattern recognition.
Classification
The chief purpose of any pattern recognition system is to classify the data
based on either a priori or statistical information. The classifiers used in this
experiment will be constructed using hidden Markov models (HMMs), which will
be the topic of the next section.
A classifier partitions the space of digital features into K disjoint subsets,
a1; ...,ak, such that for sample with feature X = (xlt ...,xg) G ak, the predicted
class is K. A learning set can be defined as:
L = {(.x1,y1),...,(xn,yn)}
Next, a classifier C can be built from the learning set as follows:
C(.,L):X-»{1,2 K)
When sequence X is observed, classifier C will decide:
C(X,L) = kifX eak
20
The system built for this experiment will focus on the construction of two
separate and distinct classifiers. One classifier will simply determine if human
motion is present by examining the observation sequence. This classifier can be
defined as above with k = 2, motion detected or motion not detected.
The second classifier will attempt to classify individual subjects for
identification purposes. This classifier can be defined as above with:
K = number of registered subjects
Hidden Markov Models (HMM)
A Hidden Markov Model (HMM) is a statistical model in which the system
being modeled is considered to be a Markov chain with unknown parameters. A
Markov chain is a stochastic process having the Markov property, meaning that
given the present state, future states are independent of the past states. A
Markov chain is considered a memory-less system and can be represented as a
finite state machine. Markov chains are stochastic in that future states will be
reached through a probabilistic process rather than a deterministic one.
Markov chains consist of various states and transitional probabilities between
those states. At each step the system may change from one state to another
state, or remain in the same state based a particular probability distribution.
When a system changes states, it is referred to as a transition. The probability
that the system will change to a particular state is called the transition probability.
Transition probabilities exist between every state and itself.
21
HMM Parameters
A Hidden Markov Model can be characterized by various known and unknown
parameters. The states that make up a regular Markov model are directly visible
to the observer, but with respect to a hidden Markov model, the states are hidden
and not directly visible. Mathematically, the set of hidden states is denoted using
set notation below:
S = {s1(..., sN, N = number of states}
The observation sequence is the observable data that is output from the model at
time f. Formally, the set of observations can be represented as :
0 = {o1;...,oTlT = number of observations}
The observation sequence described above can only contain a finite number of
discrete symbols. Formally, the set of discrete observation symbols can be
represented as:
V = {VL ..., vM, M = number of discrete symbols}
One assumption of a Markov model is that any state can follow another. Since
all states are possible, probabilities are used to determine the likelihood of one
state following another. The set of transition probabilities can be described
mathematically using set notation as shown below:
(ai,v a2,2- ••• > aN,N> N = number of states,} atJ = Pr(s t+1 = ;' | st = i)
1 < i,j < N A= { l<t<T
au > 0
X>,=1
22
Each aitj pair in the set of transition probabilities represents the probability of
transitioning from state st to state s;-. Emission probabilities describe the
probability of a particular discrete observation symbol being emitted by a
particular state. The set of emission probabilities can be described
mathematically by using set notation as shown below:
fbt(vk)\ bt{vk) = PrOfcat t\st = i)} l<i<N l<k<M bi(.vk)>0
]Tb;.(i;k) = l
B= <
Each bi(yk) represents a function which takes a particular observation symbol
and returns the probability of that symbol being emitted at state st. The last
parameter of a hidden Markov model is the start state probabilities. These
probabilities describe the state of the model at its initialization when t = 1. The
set of start state probabilities can be described mathematically using set notation
as shown below:
rnt\nt = Pr(Si = i)^
n = { nt>o
I -Each nt represents the probability of state st being the start state.
The transition, emission, and start state probabilities form a tuple (A,B,n) and
when used together, fully describe a particular hidden Markov model and is
represented by A = (A,B,n).
23
Forward Algorithm
One of the basic problems associated with hidden Markov models is
evaluation: given a particular observation sequence 0 and an HMM X, what is the
method for computing Pr (0\X), or the probability of 0 given the model? Using a
brute-force approach, this computation can be expressed as the sum of the
probabilities of all possible state sequences in the HMM:
Pr(0|A) = YS Pr(0\X) ?r(X),X = Possible hidden state sequence
This is very computationally expensive, however, as there are on the order of
Nrpossible state sequences. This clearly doesn't scale very well and is
considered impractical for most real-life problems. The solution to this problem
can be solved using a variant of the Viterbi algorithm called the Forward
algorithm.
The Forward algorithm uses a dynamic programming approach that utilizes
recursion and the idea of partial probabilities to reduce the overall computational
complexity to approximately N2T computations. Partial probabilities can be
described mathematically as:
a t(i) = Pr(ov...,ot,qt = st\X)
This can be explained as the probability that the current state is st at time t and
the partial observation olt ...,ot has been observed, given the model A. The sum
of these partial probabilities can simply be added to obtain the overall probability
Pr(0|A).
24
The Forward algorithm works in three steps: initialization, induction, and
termination. The initialization step describes the algorithm at time t = 1.
ttl(0 =,1 < i < N}
The induction step describes the approach of the algorithm between the
initialization and termination steps.
«t( / ) =
N
^ a t - i ( 0 a i j Li=i
6 y ( 0 t ) , 2 < t < T ; l < / < / V
This algorithm computes the probability that the current state is s,- and the partial
observation o1(..., ot has been observed at time t by computing the sum of the
partial probabilities of all the states at time t - 1. The termination step simply
sums all of the computed partial probabilities at time T.
Pr(0|A)= £a r ( i )
The Forward algorithm is able to provide an enormous improvement over the
naive approach, running in the order of N2T computations versus NT
computations. Another benefit of this algorithm is how it lends itself to recursion.
An efficient way to compute the forward probabilities is to start with the
termination step and work backward recursively through the inductive step until
time t = 1. The initialization step is then used to end the recursion.
Backward Algorithm
The Backward algorithm is similar to the Forward algorithm in that it used to
solve the evaluation problem. The Backward algorithm, however, works in the
opposite direction. This algorithm also uses a dynamic programming approach
25
and utilizes recursion and partial probabilities. This algorithm calculates the
probability that given an HMM, and given a state st at time t, the partial
observation ot+v ...,oT has been generated, or stated mathematically:
Pt(.0 = Pr(ot+1,...,oT\qt = si,X)
Like the Forward algorithm, the Backward algorithm works in three steps:
initialization, induction, and termination. The initialization step describes the
algorithm at time T.
/?r(0 = l , l < i < J V
The induction step describes the approach of the algorithm between the
initialization and termination steps.
,t = T-l...l,l< i <N •
The termination step simply sums all of the computed partial probabilities at time
t = 1.
N
Pr(O|A) = ^7r ijff1(0
The Backward algorithm is asymptotically equal to the Forward Algorithm.
Forward-Backward Algorithm
One of the most important problems associated with hidden Markov models is
the ability to adjust a model's parameters A = (A, B, 77) to maximize Pr (0|A).
This problem is known as learning.
It is often the case where the parameters of a hidden Markov model are
known a priori or estimated from training data. In such situations it is
26
ft(0 = ; = i
unnecessary to perform this step. However, in many cases the parameters
describing the underlying model may not be known but we would like to fit the
model parameters to a dataset. In such a case we are looking for a new model
that best fits the data or said mathematically:
X' = argmax Pr(0|A) A
Given an initial model X, it is possible to find another model X' such that
Pr (0\X') > Pr (0|A). The process of learning is accomplished using an
Expectation-Maximization algorithm called the Forward-Backward algorithm (also
known as the Baum-Welch algorithm).
The Forward-Backward algorithm requires an initial guess to be made for the
parameters. The accuracy of these initial parameters is not important, however,
more accurate estimations may lower the time this algorithm takes to converge.
Once the initial parameters have been instantiated the algorithm proceeds in two
steps: an expectation step and a maximization step. The expectation step
estimates the expected value of the unknown variables, given the current
parameter estimate. The maximization step re-estimates the distribution
parameters to maximize the likelihood of the data, given the estimates of the
expectations of the unknown variables. The expectation and maximization steps
are alternated until there is no appreciable improvement in maximum likelihood.
In order to generate a new model A' = (A', B', /7') from the initial model
X - (A,B,n), all three parameters must be re-estimated. When re-estimating the
transition probabilities: A, we need to know the probability of being in state st at
27
time t, and going to state Sj at time t - 1, given the current observation sequence
and model parameters. This can be stated in the following equation:
ft(i.;') = { p r f e = Si,qt+1 = sj | 0,X)}
This probability, called the transition probability, can be calculated as:
. ,. .. gt(Qat,jfc/(ot+i)ft+iO')
Intuitively, the transition probability re-estimation can be described as the
expected number of transitions from state st to state sj, divided by the total
number of transitions from state sit as shown in the following equation:
To help clarify the above equation, we can define:
N
This simplifies the above equation to the following:
To re-estimate the initial state probabilities, we simply need to calculate the
number of times that state st is a start state. This is just a special case of the
original equation, where time t = 1. This can be shown in the following equation:
n'i = Yi(0
The last parameter that we need to re-estimate is the emission probabilities.
Intuitively, this can described as the expected number of times in state st where
28
we observe symbol vk, divided by the total expected number of times in state su
as shown in the following equation:
b i(k)= j =f — ,8(ot>vk) = 1 if ot = vk,and 0 otherwise >
Using these parameter re-estimation formulas, we can now calculate a
improved model A' = (A'.B'.W) based on the original model A = (A,B,n)- This
re-estimation process is known as the maximization step. After this step is
completed, a expectation step is performed to calculate the forward and
backward probabilities of the given model, with the expectation that Pr (0|A') >
Pr (0\X). This process will continue in an iterative manner until there is no
appreciable improvement or Pr(0|A') - Pr(0|A) « 0.
Model Training
The Forward-Backward algorithm mentioned above will adjust a model's
parameters to fit a particular dataset. This dataset will be a digital signature or
feature that corresponds to a human motion vector. This is an example of the
supervised learning method of pattern recognition. As with any biometric system,
a user must be registered with the system before identification can take place.
For this experiment, a user will be registered by having them walk along a
predefined path for a particular amount of time. Each user will use identical
paths and training times for each test.
Model Testing
Once a series of features have been registered using the training process, we
can test the system by introducing an unknown observation sequence and then
29
determining which model best fits by finding the one that returns the maximum
likelihood. The method which we will use to calculate the probability of a testing
sequence corresponding to a particular training sequence is the Forward
algorithm. As discussed in an earlier section, the Forward algorithm computes
the probability of a particular observation (training) sequence 0, occurring given
anHMMA t lorPr(OUj).
Maximum Likelihood
Maximum likelihood criterion will be used in order to determine which training
sequence a particular testing sequence most likely matches. This can be stated
mathematically as follows:
X £ Xi, i = argmax{Pr (X | Xt)}, 1 < i < K i
Simply put, after the system has seen a complete observation sequence, it will
calculate the Forward probability that a particular HMM Xt could generate that
sequence. It will calculate the Forward probability for each HMM \it for K HMMs.
The value of Xt for which the Forward Probability is the largest, Pr(0 | Xt), will be
chosen.
30
CHAPTER 4
DATA ANALYSIS
Configuration
For this experiment, four sensor modules were custom-built and placed on a
stand. The height of the stand is fully adjustable and sensor modules can be
placed anywhere along the vertical axis to allow for maximum variability. The
figures below show a sensor module and a stand populated with four sensor
modules.
Figure 6. Sensor module.
31
Figure 7. PIR stand with four sensor modules.
Each sensor module is cabled to a microcontroller. This device receives the
analog signal, performs the analog-to-digital conversion, and the required signal
processing. The microcontroller is connected with a serial cable to a RS-232 port
on a PC. On the PC is an application built for this experiment that reads the
digital signatures and performs the training and testing phases. This application
also allows the user to interact with the system.
Microcontroller
The microcontroller used for this project is the Javelin Stamp available from
Parallax. The microcontroller is attached to the Javelin Stamp Demo board. The
Demo board also contains an onboard Sigma-Delta analog-to-digital converter,
32
which is used to convert the analog signals generated by the sensor modules to
a digital signal that can be used by the microcontroller. A Uart located on the
Demo board provides a way for the microcontroller to communicate with a PC
over a serial cable. This enables the microcontroller to transmit the binary digital
feature to a connected PC for additional processing.
The Sigma-Delta A/D converter is implemented by a combination a RC
network that is shown in the schematic below:
mmmmmmmmmimmmmmimmmBm
P9
-AW pa
22 KO
1 M F
Figure 8. Schematic of Analog-to-Digital converter.
A picture of the Demo board, Javelin Stamp, and A/D converter with the
associated wiring can be seen below:
M 22 KO
33
Figure 9. Demo board containing Javelin Stamp and ADC.
PIR Identification Application
In order to implement a pattern recognition system for identification, an
application was custom built. This application was created using C++ and
utilized the Microsoft Foundation Class (MFC) library.
The application used three threads, a GUI thread that allow the user to
interact with the interface, a worker thread that computed the HMMs, and another
worker thread that polls the Windows COM port for the signal sent by the
microcontroller. The user can choose whether a given observation sequence is a
learning event or a testing event and enter the associated parameters for each.
The application then performs the necessary calculations for either learning or
testing and outputs the received binary digital feature to the screen. The
following figure shows the user interface of the PIR identification application:
34
LEARNING PROCESS COMPLETE
ODOooo 1111111 V i 11111 Ti'i 11 oooooooooo'oobooooooooooobooooboooooooooDOOoo 111 oooooooooooo
111111111111 i i i i m i l i i i i i iiiooooooomooGaoiiioooooo'ooooooooo6ooooooi 111000000000000 •
0001111111111111111111i111111IOOOOOOOOOOOOOOOOOOOOOOOOOOOOOIOOOI11111111OOD0OOO0OO00 ;
i i 11"1ii i i 1 i'i i 1 i 11111 i 11T111 iiocraoocrad66DobDbdDooodcBOODodoQi"i 1 i i i i Ti Tictoooobdboboo:
Pifl Sensor 1
RR Sensor 2
Pifl Sensor 3
RR Sensor 4
Microcontroller Settings
Precision ^100
Threshold
HMM Learning
Number of Observations 1°°
Number of Slates j *
Name jA'on
Testing
Number of Observations
[ Start Learning j I Delete HMM
| Start |
[ Caibrate | [ OK ] Cancel |
!'.«JHH» JJEJ IJIJJUW .WHl«JJJIM..i 'LLUL f^TOMWJ.E'WW* m*!<M*J! 'JiPHCaWH!
Figure 10. PIR Human Identification Application.
Initial Testing
Using the configuration described in the previous sections, the focus then
turned to testing individuals in order to view the characteristics of their generated
waveforms.
The initial tests used four sensor modules located at a 35 in., 42 in., 48 in.,
and 54 in. from the floor, respectively, and aligned on the vertical axis. The
output from each sensor was fed through an analog-to-digital converter and then
sent to the microcontroller. The microcontroller processed each signal by
subtracting 127 from each sample and then taking the absolute value, which
results in a signal whose amplitude that is directly proportional to the generated
voltage on its respective sensor. The microcontroller sampled the signal every
100 ms or 10 times a second. The sensor modules were placed in the middle of
a room, with a path marked with tape located perpendicularly to the sensors.
35
This path is two feet away from the sensors at its closest point. Below is a
diagram showing the position of the sensors and the walking path:
Sensor
? CM
* 8 ft +~4 8 ft-
Path
Figure 11. Experiment walking path.
The subject was instructed to walk in a straight line along the path, and then turn
around once the end of the path was reached. The subject walked for 20
seconds, which produced 200 samples. The following four figures show the
signals generated for each of the four sensors:
36
Sensor 1
•Sensor 1
r H < 7 > r ^ i n m r H C T i r ^ L n m < H a , i t ^ u " ) m < - i C T i r * L n m < H a i r ^ m r r > r n r v i m ^ - ^ j - L O t o i ^ o o o o f f i O r H i N r M r o ^ - L n t o i D r ^ o o a i ( H r H r ^ r - l i H r H r - l r H i H r H r H T H
Figure 12. Signal generated from sensor 1.
Sensor 2 40
35
30
25
20
15
10
•Sensor 2
TnTmrrnTTrr in 11111111 rtrnTiTn
» - i r \ i m « 3 - ^ - L r i i > ° r ^ o o o o C T i O r - i < N ( N r o ^ f u " i i o i o r ^ o o < T i
Figure 13. Signal generated from sensor 2.
37
Sensor 3 50
•Sensor 3
< - i r \ i m « t f « 3 - L n u 3 r ^ o o o o c i o < - i ( N < N m ^ j i u - > i D i o r ^ o o o i
Figure 14. Signal generated from sensor 3.
Sensor 4 30
25
20
15
10
5
•Sensor 4
/ * * *
» H a i r ^ . L n r r ) r - ( ( n r ~ L f i m t H C T i r « - L n r r ) r - i o ^ r ^ L n m T - i C T > r ^ L n r r i
Figure 15. Signal generated from sensor 4.
In the figures above, the amplitude is directly proportional to the subject's
proximity to the sensor. High frequency noise dominates the areas between the
peaks where little or no motion has been detected.
38
Intuitively, it seems that due to the characteristic nature of a person's gait,
each person should affect a sensor field in a unique way. As a person moves
through a sensor field, the magnitude and spread of the voltage generated on a
particular sensor is proportional to the infrared energy detected over time. The
amount of energy depends on the movement and composition of the body parts
that the sensor is focused on. This can affect the signal in two distinct ways.
The amplitude of the peaks will be more if the sensor is pointed towards the
warmer areas of the body, such as the torso. A person's height is one factor that
will affect whether a sensor is pointed near the warmer areas of the body or
colder areas such as the head and legs. We can compare the amplitudes of two
or more signals by calculating the mean of each signal. The spread of a signal
will be determined by a number of factors, such as the speed of the walker, the
swing of the arms, and the shape of the body. By calculating the standard
deviation of a signal, we can measure its spread. Therefore, if it is assumed that
the noise is constant in every signal, we may be able to determine if the signal is
unique by comparing the mean and standard deviation of the signals generated
by multiple subjects. The next two figures show bar charts that represent the
mean and standard deviation, respectively, of three different subjects. Each
subject is represented by four bars, corresponding to each of the four sensors.
39
Gl
Mean
G2 Jl J2 A l A2
mSensor 1
Sensor 2
DSensor 3
• Sensor 4
Gl
Figure 16. Sample means for three subjects.
Standard Deviation
G2 Jl J2 Al A2
mSensor 1
Sensor 2
• Sensor 3
• Sensor 4
Figure 17. Sample standard deviations for three subjects.
It can be seen in the charts that the mean and standard deviations of the signals
representing a particular subject are consistent between trials. This
demonstrates that these signals are repeatable. It can also be seen that the
40
signals representing a subject are dissimilar from that of the other subjects. This
demonstrates that these signals may be characteristic of the subject that
generated them.
Experiment
The experiment was carried out using four subjects. Each subject conducted
a walk of particular duration to train the system and then performed five walks
each of varying durations to test the system.
The variables of the experiment are the time taken to train the system, and
the time taken to test the system. There were two different training times used,
50 sec (500 samples) and 100 sec (1000 samples). For each training time, there
were four different testing times, 500 sec, 200 sec, 100 sec, and 50 sec. Each
subject tested at each level five times. The other HMM parameters, such as
states, were kept constant throughout the experiment. The results of the
experiment are shown in the tables below:
Table 1 Experiment Results (Training Set = 500), (Testing Set = 500)
Name Aron Ghada Josh Shirin
Aron 80%
20%
Ghada 20% 80%
)le 2 Experiment Results (Training Set =
Josh
20% 100%
= 500),
Shirin
80%
(Testing Set = 2
Name Aron Ghada Josh Shirin
Aron 60%
20% 40%
Ghada 40% 80%
Josh
20% 40%
Shirin
40% 60%
41
Table 3 Experiment Results (Training Set = 500), (Testing Set = 100)
Name Aron Ghada Josh Shirin
Aron 60%
20% 60%
Ghada
60%
Table 4 Experiment Results (Training Set
Josh 40% 4 0 % 60%
= 500).
Shirin
20% 4 0 %
(Testing Set = 50)
Name Aron Ghada Josh Shirin
Aron 60%
60%
Ghada
100% 4 0 %
Josh 4 0 %
60%
Shirin
4 0 %
Table 5 Experiment Results (Training Set = 1000), (Testing Set = 500)
Name Aron Ghada Josh Shirin
Aron 100%
4 0 % 60%
Ghada Josh
100% 60% 20%
Table 6 Experiment Results (Training Set = 1000),
Shirin
20%
(Testing Set = 200)
Name Aron Ghada Josh Shirin
Aron 60%
20% 80%
Ghada Josh 4 0 %
100% 20%
Shirin
60% 20%
Table 7 Experiment Results (Training Set = 1000), (Testing Set = 100)
Name Aron Ghada Josh Shirin
Aron 40%
20%
Ghada Josh 60%
100% 80% 60%
Shirin
20% 20%
42
Table 8 Experiment Results (Training Set = 1000), (Testing Set = 50)
Name Aron Ghada Josh Shirin
Aron 60%
40% 20%
Ghada
100%
Josh 40%
60% 20%
Shirin
60%
From each of the tables above, it can be seen that the longer testing times
generally result in a higher probability of positive identification. The two training
times, however, didn't seem to have much of an effect one way or the other on
the results. There is a trade-off between short testing times and a high
probability of identification. It is desirable to have as short of a testing time as
possible so that a person could be identified quickly. However, with a short
testing time there is a relatively small amount of samples compared to its
corresponding training sequence, which could limit the system's precision. One
interesting note about the results show that while the results are much better at
when a test with 500 samples are used, there is no noticeable drop-off in
identification rate from tests that used 200 samples down to 50 samples. In fact,
the test with 50 samples slightly out performed some of the longer tests.
43
CHAPTER 5
CONCLUSIONS
The goals of this paper were threefold; two determine if the digital features
generated by a motion sensor are characteristic of human motion, to build a
classifier that can detect human presence, and build another classifier that can
perform human identification. It is not completely certain that the digital features
generated by the motion sensors used in this experiment and using the signal
processing techniques described in this paper, are truly a characteristic measure
of the human gait.
The second goal was to design a classifier that can detect the presence of a
human in a room. It was demonstrated that the hardware and software
developed for this experiment certainly was successful in implementing a system
that could accurately detect human motion. The amount of motion necessary for
detection is minimal enough that even a human attempting to stand still would
generate a motion event. This system could be used for numerous applications,
much like conventional motion detection systems.
The third goal of this paper was to design a classifier that could be used a
biometric device; able to perform the complex task of human identification.
Ultimately, successfully achieving this goal is tied to the accomplishment of the
first goal, which is to fulfill the task of generating a characteristic digital feature.
44
It's impossible to say with any level of confidence that this goal was achieved,
however, some of the results seemed promising. The random chance of positive
identification in any given trial with four subjects would be one in four, or 25%.
While the results in most of the trials were far from perfect, none had an overall
identification rate less than 50%. Additionally, out of the 32 individual trials run in
this experiment, only three had positive identification rates that were lower than
25%. The most successful trials were the two that used 500-sample testing sets.
Notably, the trial characterized by a 500-sample training set and a 500-sample
testing set was able to achieve an overall positive identification rate of 85%.
Although the number of trials run is way too small to be free of statistical noise, it
is still hard to imagine an outcome of 85% being attributed to random chance.
It is uncertain that this application, if designed properly, would be suitable as
a standalone biometric system. This question would have to be the topic of a
future paper. One major limitation of the implementation described in this paper
is that there is no easy way to determine if the subject being tested was ever
trained to begin with. Using hidden Markov models as a probability model, the
system simply chooses the trained model that has the highest probability of
matching the current observation sequence. In order to provide a way to
numerically determine that the current observation sequence does not
correspond to any trained model, some sort of adaptive threshold would have to
be used. It seems apparent that the real use and power of a system such as the
one presented would be as an alternate identification mechanism that could pair
45
in tandem with other biometric systems as a way to increase the overall
likelihood of correct authentication.
Ultimately, future work must be done in this area before any judgment could
be made on the subject matter. The quality of the electronics used in the sensor
modules, analog-to-digital conversion, and signal processing could vastly be
improved in production than what was used for this experiment. The method of
generating the digital feature used in this experiment is also rather simple and
rudimentary and could most likely be improved. Lastly, other statistical models,
such as principle components analysis (PCA), neural networks, etc. could
possibly lead to better results and therefore, should be explored.
46
BIBLIOGRAPHY
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Petruzella, Frank D. Essentials of Electronics: A Survey. New York, NY: Glencoe/McGraw-Hill, 1993.
Agresti, Alan, Franklin, Chris. Statistics: The Art and Science of Learning from Data. 2nd edition. Upper Saddle River, NJ: Pearson Prentice Hall, 2007.
Serway, Raymond A., Faughn, Jerry S. College Physics. 6th edition. Volume 1. Pacific Grove, CA: Brooks/Cole-Thomson Learning, 2003.
Serway, Raymond A., Faughn, Jerry S. College Physics. 6th edition. Volume 2. Pacific Grove, CA: Brooks/Cole-Thomson Learning, 2003.
Al Williams Consulting. Javelin Stamp User's Manual. Version 1.1.
J.S. Fang, Q. Hao, D. Brady, B. Guenther, K. Hsu. Real-time human identification using a pvroelectric detector array and hidden Markov models.
N. Kakuta, S. Yokoyama, M. Nakamura. Estimation of radiative heat transfer using a geometric human model. IEEE Trans. Biomed. Eng. 48, 324-331, 2001.
A. Kale, N. Cuntoor, B. Yegnanarayana, A.N Rajagopalan, R.Chellappa. Gait analysis for human identification.
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47
VITA
Graduate College University of Nevada, Las Vegas
Aron Edward Suppes
Home Address: 10091 Cranbrook Falls Ct Las Vegas, NV 89148
Degrees: Bachelor of Science, Computer Science, 2005 Hawaii Pacific University
Thesis Title: Human Identification Using Pyroelectric Sensors
Thesis Examination Committee: Chairperson, Dr. Evangelos A. Yfantis, Ph. D. Committee Member, Dr. Jan Pedersen, Ph. D. Committee Member, Dr. Laxmi P. Gewali, Ph. D. Graduate Facility Representative, Dr. Georg Mauer, Ph. D.
48